
The \(\lambda \) -minimal weight space, denoted \(Z_{\min }= Z(Y,\lambda )_{\min }\)  is the closed subscheme
\(Z(Y,\lambda )_{\min }:=Y \cap \mathbb {P}(V_{\min })=\left\lbrace  y \in Y^{\lambda (\mathbb {G}_m)} : \lambda (\mathbb {G}_m) \text{ acts on } \mathcal {L}^*|_y \text{ with weight } \omega _{\min } \right\rbrace ,\) 

The \(\lambda \) -attracting open set, denotedIn [1]}, the open scheme \(Y_{\min }\)  is denoted \(Y_{\min }^0\) . \(Y_{\min }= Y(\lambda )_{\min }\) , is the open subscheme
\(Y(\lambda )_{\min }:=\lbrace y\in Y \mid p(y) \in Z_{\min }\rbrace  \quad \mbox{and } \quad p(y) := \lim _{\begin{array}{c} t \rightarrow 0\\ t \in \mathbb {G}_m \end{array}} \lambda (t) \cdot y \quad \mbox{ for } y \in Y,\) 

The \(\lambda \) -retraction is \(p : Y_{\min } \rightarrow Z_{\min }\) , given by \(p(y):= \lim _{t \rightarrow 0} \lambda (t) \cdot y\) ,

The (semi)stable minimal weight space is \(Z_{\min }^{(s)s}:=Z_{\min }^{\overline{L}-(s)s}\)  and we let \(Y_{\min }^{(s)s} := p^{-1}(Z_{\min }^{(s)s})\) .


